The perimeter of the rectangle is 12 m, and its area is 8 m square. You need to find the sides of the triangle.

We are given a rectangle and know the perimeter and area of this rectangle. In order to find the lengths of the sides of a rectangle, we will compose and solve the system of equations:

P = 2 (a + b);

S = ab;

System:

a + b = 6;

ab = 8.

We solve using the substitution method:

a = 6 – b;

ab = 8.

We substitute the expression from the first into the second equation and solve:

a = 6 – b;

b (6 – b) = 8.

-b ^ 2 + 6b – 8 = 0;

b ^ 2 – 6b + 8 = 0;

We are looking for the discriminant of the equation:

D = (-6) ^ 2 – 4 * 1 * 8 = 36 – 32 = 4;

b1 = (6 + 2) / 2 = 8/2 = 4;

b2 = (6 – 2) / 2 = 4/2 = 2.

A set of systems:

System 1:

a = 6 – 4 = 2;

b = 4;

System 2: a = 6 – 2 = 4;

b = 2.

Answer: 2 and 4 meters of the length of the sides of the rectangle.